free-gmat-downloads_Vedic mathematics1
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(786-002) or (998-214) / (214X2)
786 -214 [ BASE 1000]
998 -002
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784 / 428
Answer is 784428
Example. 2: Find 994 X 988.
Here base is 1000
994 -006 [ BASE 1000]
988 -012
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(786-002) or (998-214) / (214X2)
994 -006 [ BASE 1000]
988 -012
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982 / 072
Answer is 982072
Example. 3: Find 750 X 995.
Here base is 1000
750 -250 [ BASE 1000]
995 -005
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(750-005) or (995-250) / (250X005)
750 -250 [ BASE 1000]
995 -005
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745 / 1250
Since the base is 1000, we write down 250 and carry 1 over
to the left giving us 745 / 1250 = (745+1) / 250
Answer is 746250
Assignments
Find the following |
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Q1. |
993 X 998 |
Q2. |
815 X 998 |
Q3. |
987 X 994 |
Q4. |
985 X 998 |
Q5. |
995 X 999 |
Q6. |
688 X 998 |
Q7. |
999 X 999 |
Q8. |
872 X 998 |
Assignments Answers
Find the following |
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Q1. |
993 X 998 =991014 |
Q2. |
815 X 998 =813370 |
Q3. |
987 X 994 =981078 |
Q4. |
985 X 998 =983030 |
Q5. |
995 X 999 =994005 |
Q6. |
688 X 998 =686624 |
Q7. |
999 X 999 =998001 |
Q8. |
872 X 998 =870256 |
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Chapter 4 : Multiplication
4.2 : Multiplication near to the base
4.2.2 Both the numbers are higher than the base.
The method and rules : The only difference is the positive deviation. Instead of cross?subtract, we follow cross?add.
Example.1: Find 13X12.
Base is 10
13 3 [ BASE 10]
12 2
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(13 + 2) or (12 + 3) / (3 X 2)
13 3 [ BASE 10]
12 2
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15 / 6
Answer is 156
Example.2: Find 18X14.
Base is 10
18 8 [ BASE 10]
14 4
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(18 + 4) or (14 + 8) / (8 X 4)
18 8 [ BASE 10]
14 4
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22 / 32
Since the base is 10, we write down 2 and carry 3 over to the left giving us 22 / 32 = (22+3) / 2
Answer is 252
Example 3: Find 104 X 102
Here base is 100
104 04 [ BASE 100]
102 02
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(104 + 02) or (102 + 04) / (04 X 02)
104 |
04 |
[ BASE 100] |
102 |
02 |
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106 / 08
Answer is 10608
Example. 4: Find 1275 X 1004.
Here base is 1000
1275 275 [ BASE 1000]
1004 004
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(1275 + 004) or (1004 + 275) / (275 X 004)
1275 275 [ BASE 1000]
1004 004
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1279 / 1100
Since the base is 1000, we write down 100 and carry 1 over to the left giving us 1279 / 1100 = (1279+1) / 100
Answer is 1280100
Assignments
Find the following |
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Q01. |
11 X 14 |
Q02. |
15 X 10 |
Q03. |
12 X 13 |
Q04. |
11 X 11 |
Q05. |
101 X 104 |
Q06. |
121 X 104 |
Q07. |
107 X 103 |
Q08. |
134 X 102 |
Q09. |
1004 X 1009 |
Q10. |
1115 X 1004 |
Q11. |
1005 X 1003 |
Q12. |
1035 X 1002 |
Assignments Answers
Find the following |
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Q01. |
154 |
Q02. |
150 |
Q03. |
156 |
Q04. |
121 |
Q05. |
10504 |
Q06. 12584 |
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Q07. |
11021 |
Q08. 13668 |
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Q09. |
1013036 |
Q10. |
1119460 |
Q11. |
1008015 |
Q12. |
1037070 |
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Chapter 4 : Multiplication
4.2 : Multiplication near to the base
4.2.3.1.1 Bar Numbers and application
Look at the following Subtractions
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9 = 10 ?1 = 11
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8 = 10 ?2 = 12
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7 = 10 ?3 = 13
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6 = 10 ?4 = 14
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5 = 10 ?5 = 15
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4 = 10 ?3 = 16
9 is same as 10 - 1 , and this may be written as one ten in the ten?s column and take away 1 in the units column.
8 is same as 10 - 2 , and this may be written as one ten in the ten?s column and take away 2 in the units column.
More examples
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98 = 100 ? 2 = 102
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196 = 200 ? 4 = 204
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32 = 30 ? 2 = 28
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145 = 140 ? 5 = 135
A Viniculum Number OR Bar Number is a take away or minus number.
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28 = 30 ? 2 = 32 because 28 is 2 less than 30.
Thirty viniculum two is 28.
Example 1.
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Bar number of 47 can be found by 47 = 50 ? 3 = 53 One more than 4 is 5 and the complement of 7 is 3.
It is like telling the time when we say ?Five to six? instead of 5:55
To change a number back into its ordinary form, write down the complement of the viniculum number and subtract 1 from the next digit to the left
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To convert Viniculum 53
Complement of 3 is 7 and 5 ? 1 is 4 give us the original number as 47.
Example 2
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To convert 75
Complement of 5 is 5 and 7-1 gives 6
The original number is 65
To change a tens column digit into a Viniculum we use same method. The digit is replaced by its complement and the digit to the left is increased by 1
Example 3
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Convert Viniculum 174
The complement of 7 is 3 and 1+1 = 2
This is saying that one hundred seven tens and four units is the same as two hundreds minus three tens and 4 units.
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Viniculum 174 is 234
To change a tens column digit into a viniculum we use same method. The digit is replaced by its complement and the digit to the left is increased by 1
Example 4
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Convert Viniculum 632
The complement of 3 is 7 and 6 ? 1 = 5 . Answer is 572
Some Numbers may have more than one Viniculum number
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3 3 2 4 5 8 2 = 2 7 2 4 4 2 2
4.2.3.1.2 Adding and subtracting Viniculum numbers
Viniculum numbers are added or subtracted just like ordinary numbers.
_ _ _
3 + 2 =5
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5 - 2 |
=3 |
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12 + 3 = 9
Assignments
Find the following
Q1. Change units digit into viniculum number for 46
Q2. Change the following numbers back to ordinary form
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1. |
12 |
2. |
51 |
3. |
42 |
4. |
85 |
Q3. Change tens digit into viniculum number for 621
Q4. Change the following numbers back to ordinary form
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1. |
4131 |
2. |
3333 |
3. |
7151 |
4. |
65321 |
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Q5. |
Find the following |
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1. 3 + 2 |
2. 8 - 4 |
3. 2 - 2 |
4. 6 + 2 |
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Assignments Answers
Find the following
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Q1. |
54 |
Q2. Change the following numbers back to ordinary
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form |
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1. |
8 |
2. |
49 |
3. |
38 |
4. |
75 |
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Q3. |
781 |
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Q4. Change the following numbers back to ordinary form
1. |
3929 |
2. |
2727 |
3. |
6949 |
4. |
55281 |
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Q5. |
Find |
the following |
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1. |
5 |
2. |
4 |
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0 |
4. |
4 |
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www.fastmaths.com
Chapter 4 : Multiplication
4.2 : Multiplication near to the base
4.2.3.1.1 Bar Numbers and application
Example.1: Find 13 X 7.
Base is 10
13 3 [ BASE 10 ]
7-3
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10 / 9
One deviation is positive and the other is negative. So the product of deviations becomes negative. So the right hand side of the answer obtained will therefore have to be subtracted.
Using ?To change a tens column digit into a Viniculum we use same method. The digit is replaced by its complement and the digit to the left is decreased by 1?
Complement of 9 is 1 and 10 is decreased by 1
13 3 [ BASE 10 ]
7 -3
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(10-1) / Complement of 9 = 91
Answer is 91
Example.2: Find 108 X 94.
Base is 100
108 08 [ BASE 100 ]
94 -06
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102 / 48
Complement of 48 is 52 and 102 is decreased by 1 (102-1) / Complement of 48 = 10152
Answer is 10152
Example.3: Find 998 X 1025.
Base is 1000
998 |
-002 [ BASE 1000 ] |
1025 |
025 |
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1023 / 050
Complement of 50 is 950 and 1023 is decreased by 1 (1023-1) / Complement of 50 = 1022950
Answer is 1022950
Assignments